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Ideal Paraconsistent Logics

Abstract

We define in precise terms the basic properties that an ‘ideal propositional paraconsistent logic’ is expected to have, and investigate the relations between them. This leads to a precise characterization of ideal propositional paraconsistent logics. We show that every three-valued paraconsistent logic which is contained in classical logic, and has a proper implication connective, is ideal. Then we show that for every n > 2 there exists an extensive family of ideal n-valued logics, each one of which is not equivalent to any k-valued logic with k < n.

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Correspondence to A. Avron.

Additional information

Dedicated to Professor Ryszard Wójcicki on the occasion of his 80th birthday

Special issue in honor of Ryszard Wójcicki on the occasion of his 80th birthday

Edited by J. Czelakowski, W. Dziobiak, and J. Malinowski

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Arieli, O., Avron, A. & Zamansky, A. Ideal Paraconsistent Logics. Stud Logica 99, 31 (2011). https://doi.org/10.1007/s11225-011-9346-y

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Keywords

  • Paraconsistent logics
  • ideal paraconsistency
  • many-valued logics